MOTIVATION: Short-read single-cell RNA-sequencing (scRNA-seq) has been used to study cellular heterogeneity, cellular fate, and transcriptional dynamics. Modeling splicing dynamics in scRNA-seq data is challenging, with inherent difficulty in even the seemingly straightforward task of elucidating the splicing status of the molecules from which sequenced fragments are drawn. This difficulty arises, in part, from the limited read length and positional biases, which substantially reduce the specificity of the sequenced fragments. As a result, the splicing status of many reads in scRNA-seq is ambiguous because of a lack of definitive evidence. We are therefore in need of methods that can recover the splicing status of ambiguous reads which, in turn, can lead to more accuracy and confidence in downstream analyses. RESULTS: We develop Forseti, a predictive model to probabilistically assign a splicing status to scRNA-seq reads. Our model has two key components. First, we train a binding affinity model to assign a probability that a given transcriptomic site is used in fragment generation. Second, we fit a robust fragment length distribution model that generalizes well across datasets deriving from different species and tissue types. Forseti combines these two trained models to predict the splicing status of the molecule of origin of reads by scoring putative fragments that associate each alignment of sequenced reads with proximate potential priming sites. Using both simulated and experimental data, we show that our model can precisely predict the splicing status of many reads and identify the true gene origin of multi-gene mapped reads. AVAILABILITY AND IMPLEMENTATION: Forseti and the code used for producing the results are available at https://github.com/COMBINE-lab/forseti under a BSD 3-clause license.